Improper fractions can be converted to mixed numbers without using long division.
The key steps involve breaking down the numerator into a sum of two numbers, where one is the largest multiple of the denominator less than the numerator.
Example: 11/4
Break down: 11 can be written as 8 + 3.
8/4 is 2 (since 8 is the highest multiple of 4 below 11).
Therefore, 11/4 as a mixed number is 2 and 3/4.
Example: 17/5
Break down: 17 can be written as 15 + 2.
15/5 is 3.
Therefore, 17/5 as a mixed number is 3 and 2/5.
Example: 53/6
Find the highest multiple of 6 under 53:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48.
48 is the highest multiple of 6 under 53.
Break down: 53 can be written as 48 + 5.
48/6 is 8.
Therefore, 53/6 as a mixed number is 8 and 5/6.
Example: 45/7
Find the highest multiple of 7 under 45:
Multiples of 7: 7, 14, 21, 28, 35, 42.
42 is the highest multiple of 7 under 45.
Break down: 45 can be written as 42 + 3.
42/7 is 6.
Therefore, 45/7 as a mixed number is 6 and 3/7.
Summary
To convert improper fractions to mixed numbers:
Identify the highest multiple of the denominator less than the numerator.
Break down the numerator into this multiple plus any remainder.
Divide the multiple by the denominator to find the whole number part.
The remainder over the original denominator becomes the fractional part.
Verify by converting the mixed number back to an improper fraction.